A mesh includes elements that are typically simple shapes such as tetrahedrons, hexahedrons, prisms, and pyramids. These simple shapes have faces, edges, and vertices. A mesh includes a collection of these elements and a mathematical description of the relationship between the nodes, edges, and faces of the elements. In the numerical analysis of physical systems (e.g., industrial systems or volumetric objects), complicated three-dimensional shapes may be broken down into (i.e., approximated by) a mesh representation. The mesh representation may subsequently be used in setting up and solving equations for finite element analysis, which may include the numerical solution of partial differential equations. Other analysis methods are used in other examples. Mesh-based analysis techniques are used widely in the fields of computational fluid dynamics, aerodynamics, electromagnetic fields, civil engineering, chemical engineering, naval architecture and engineering, and other related fields.